Radius of Circular Section of Torus given Lateral and Total Surface Area of Torus Sector Calculator

Formula Used:

\[ r = \sqrt{\frac{TSA_{sector} - LSA_{sector}}{2\pi}} \]

Radius of Circular Section of Torus (r):

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1. What is Radius of Circular Section of Torus?

The radius of circular section of a torus is the distance from the center of the circular cross-section to any point on its circumference. It's a fundamental parameter in torus geometry that helps define the size and shape of the torus.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \sqrt{\frac{TSA_{sector} - LSA_{sector}}{2\pi}} \]

Where:

\( r \) — Radius of circular section of torus (m)
\( TSA_{sector} \) — Total surface area of torus sector (m²)
\( LSA_{sector} \) — Lateral surface area of torus sector (m²)
\( \pi \) — Mathematical constant pi (≈3.14159)

Explanation: The formula calculates the radius by finding the difference between total and lateral surface areas, then dividing by 2π and taking the square root.

3. Importance of Radius Calculation

Details: Calculating the radius of circular section is essential for understanding torus geometry, volume calculations, surface area computations, and various engineering applications involving toroidal shapes.

4. Using the Calculator

Tips: Enter both surface area values in square meters. Ensure TSA > LSA and both values are positive. The calculator will compute the radius automatically.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between total and lateral surface area?
A: Total surface area includes all surfaces of the torus sector, while lateral surface area only includes the curved surface area excluding the base areas.

Q2: What units should I use for input values?
A: Use consistent units (preferably meters and square meters) for accurate results. The calculator assumes SI units.

Q3: Can this calculator handle negative values?
A: No, surface area values must be positive numbers, and TSA must be greater than LSA.

Q4: What if I get an error message?
A: Check that TSA > LSA and both values are positive numbers. The difference TSA-LSA must be positive for the square root calculation.

Q5: How accurate are the results?
A: Results are accurate to 6 decimal places, providing precise calculations for engineering and mathematical applications.